Instability in Geophysical Flows

An Open Access overview of physical processes that generate instability in geophysical flows, emphasising numerical methods and simple rules to predict instability.

William D. Smyth (Author), Jeffrey R. Carpenter (Author)

9781108703017, Cambridge University Press

Paperback / softback, published 11 April 2019

338 pages, 144 b/w illus. 115 colour illus.
24.5 x 17 x 2.4 cm, 0.86 kg

'… large number of analytical and numerical exercises, make the book suitable for use in teaching a graduate or upper-level undergraduate course on the subject of geophysical ?uid dynamics. The material covered would be helpful both to atmospheric science students and researchers who wish to understand the mathematical theory and numerical simulation techniques and to applied mathematics students and researchers who wish to learn more about the geophysical processes and the mechanisms that lead to the instabilities.' Lucy J. Campbell, Mathematical Reviews Clippings

Instabilities are present in all natural fluids from rivers to atmospheres. This book considers the physical processes that generate instability. Part I describes the normal mode instabilities most important in geophysical applications, including convection, shear instability and baroclinic instability. Classical analytical approaches are covered, while also emphasising numerical methods, mechanisms such as internal wave resonance, and simple `rules of thumb' that permit assessment of instability quickly and intuitively. Part II introduces the cutting edge: nonmodal instabilities, the relationship between instability and turbulence, self-organised criticality, and advanced numerical techniques. Featuring numerous exercises and projects, the book is ideal for advanced students and researchers wishing to understand flow instability and apply it to their own research. It can be used to teach courses in oceanography, atmospheric science, coastal engineering, applied mathematics and environmental science. Exercise solutions and MATLAB® examples are provided online. Also available as Open Access on Cambridge Core.

Preface
Part I. Normal Mode Instabilities: 1. Preliminaries
2. Convective instability
3. Instabilities of a parallel shear flow
4. Parallel shear flow: the effects of stratification
5. Parallel shear flow: the effects of viscosity
6. Synthesis: viscous, diffusive, inhomogeneous, parallel shear flow
7. Nonparallel flow: instabilities of a cylindrical vortex
8. Instability in a rotating environment
9. Convective instability in complex fluids
10. Summary
Part II. The View Ahead: 11. Beyond normal modes
12. Instability and turbulence
13. Refining the numerical methods
Appendix A. Homework exercises
Appendix B. Projects
List of illustrations
List of tables
References
Index.

Subject Areas: Mechanics of fluids [TGMF], Meteorology & climatology [RBP], Oceanography [seas RBKC], Atmospheric physics [PHVJ], Geophysics [PHVG], Fluid mechanics [PHDF]